Lecture 19Lecture 19--Magnetic Properties of MaterialsMagnetic Properties of MaterialsChapter 35 Chapter 35 --Tuesday March 27thTuesday March 27th•Finish off Ampere’s law•Review of magnetic dipoles•The forces on magnetic dipoles•Atomic and nuclear magnetism•Magnetization and Magnetic materialsReading: pages 801 thru 811 (up to section 35Reading: pages 801 thru 811 (up to section 35--6) in HRK6) in HRKRead and understand the sample problemsRead and understand the sample problemsWebAssign deadline will be Tuesday April 3WebAssign deadline will be Tuesday April 3rdrdat 11:59pmat 11:59pmThis homework will be on both This homework will be on both ChsChs. 34 (Thu.) and 35. 34 (Thu.) and 35Ch. 35: E23, P8; Ch. 35: E23, P8; Ch. 34: E16, E23, E26, E31Ch. 34: E16, E23, E26, E31Practice problems from the text:Practice problems from the text:Ch.35Ch.35--E11, E21, P1; Ch.34E11, E21, P1; Ch.34--E3, E11, E27, E29, P7, P9E3, E11, E27, E29, P7, P9Review of AmpReview of Ampèèrere’’s Laws Law()12oenc odi iiμμ⋅ ==−∫BsGGvcos ;dBdsθ⋅ =∫∫BsGGvvenc jSid= ⋅ = Φ∫jAGGRightRight--handhand--ruleruleMaxwellMaxwell’’s 3rd equation (a.k.a. Amps 3rd equation (a.k.a. Ampèèrere’’s Law)s Law)The fundamental theorem of calculus:The fundamental theorem of calculus:() ()2121xxdfdx fx fxdx⎛⎞=−⎜⎟⎝⎠∫() ()2121fd f f∇⋅ = −∫rrrr rGGGGGThis gives us two new integral theorems known as the ‘divergence theorem’ (sometimes called Gauss’ law) and the ‘curl theorem’ (also known as Stokes’ theorem).()volume surfacedV d∇⋅=⋅∫∫EEAGGGv()surface boundarylinedd∇×⋅ = ⋅∫∫EA ElGGGGvGauss:Stokes:MaxwellMaxwell’’s 3rd equation (a.k.a. Amps 3rd equation (a.k.a. Ampèèrere’’s Law)s Law)()oSSdddμ⋅ = ∇× ⋅ = ⋅∫∫ ∫Bs B A jAGGGGGGvThe fundamental theorem of calculus:The fundamental theorem of calculus:oμ∇×=BjGGORORThe Torque on a Current LoopThe Torque on a Current Loop()()ˆ cosiA niUBμθ=×=×=×= −⋅= −BABBBGGGGGGGGτμμMagnetic dipole moment:i= AGGμIf the loop has N turns:Ni= AGGμDimensions: Amp·meter2(A ·m2) or Joule/tesla (J/T)The Magnetic Field of a DipoleThe Magnetic Field of a Dipole2, and iA A Rμπ⎡⎤==⎣⎦()220003/23322222iR i RBzzRzμμπμμππ==+ElectricdipoleMagneticdipoleBarmagnet3012pEzπε=(P. 26-1)At large distances (At large distances (zz>> >> RR) along the ) along the zz--axisaxisAtomic and Nuclear MagnetismAtomic and Nuclear MagnetismBohr theory of the atomBohr theory of the atom2424 9.27 10 J/Tatom Beeeehmmμμπ−≅ ===×=Atomic and Nuclear MagnetismAtomic and Nuclear MagnetismElectrons, protons and Electrons, protons and neutrons also spinneutrons also spin242727269.27 10 J/T5.05 10 J/T9.28 10 J/T1.41 10 J/Telectron Bnucleus Nneutronprotonμμμμμμ−−−−== ×≈ =×=×=×NNSSMagnetic ResonanceMagnetic ResonanceGFGddt==×LrFGGGGτSame true for electrons, Same true for electrons, proton and neutrons in a proton and neutrons in a magnetic fieldmagnetic field47.6 MHz/T414 GHz/T4NpeeddtBeBfhmfeBmfeBmμπππ=×== ≈≈≈≈≈BGGGGτlμMagnetizationMagnetization00000/Mmeμκκ=+=+⎡⎤==⎢⎥⎣⎦BB BBB MBBEEGG GGG GGGGG()001mμκ= −MBGGDefinition of M:Definition of M:net magnetic moment per unit volumenet magnetic moment per unit volumenVV==∑MGGGμμMagnetic properties of materialsMagnetic properties of materialsParamagnetismParamagnetismVery similar similar to the behavior of dielectrics, with one Very similar similar to the behavior of dielectrics, with one VERY important difference VERY important difference --M//BM//B00..()1or 1 0mmκκ⇒ > − >κκmmis strongly temperature dependent. Thermal motion tends to disris strongly temperature dependent. Thermal motion tends to disrupt upt alignment. Actual behavior fairly straightforward to derive in aalignment. Actual behavior fairly straightforward to derive in athermal thermal physics course. The law was first discovered by Pierre Curie in physics course. The law was first discovered by Pierre Curie in 1895:1895:001BBBBMCTkTμ⎛⎞⎟⎜⎟=<<⎜⎟⎜⎟⎜⎝⎠Magnetic properties of materialsMagnetic properties of materialsParamagnetismParamagnetismnmaxNMVVμ==∑GμMagnetic properties of materialsMagnetic properties of materialsDiamagnetismDiamagnetismFaradayFaraday’’s and Lenzs and Lenz’’s laws (Ch. 34) s laws (Ch. 34) BSdddtdddtεΦ⋅ ==−= −⋅∫∫EsBAGGGGvTherefore, just like the behavior of dielectrics, including the Therefore, just like the behavior of dielectrics, including the fact that M fact that M is antiparallel to Bis antiparallel to B00. However, the definition of . However, the definition of κκmmis the same as for a is the same as for a paramagnet:paramagnet:()001mμκ= −MBGG()1or 1 0mmκκ⇒ < − <RepulsionRepulsionMagnetic properties of materialsMagnetic properties of materialsDiamagnetismDiamagnetismFor most ordinary substances, (For most ordinary substances, (κκmm−−1) is very small, i.e. 1) is very small, i.e. −−1010−−66to to −−1010−−5.5.However, there is one very important exception:However, there is one very important exception:Perfect diamagnetismPerfect diamagnetism()11or 0 mmκκ− = −=00mκ⇒ ==BBGGMeissner effectMeissner effectDiamagnetic levitationDiamagnetic levitation• Molecular diamagnetism– Common to all matter– Usually obscured by other forms of magnetism• Becomes apparent in strong magnetic fields• Study effects of micro-gravity– Crystal growth– Plant growthhttp://www-hfml.sci.kun.nl/hfml/levitate.htmlhttp://www.nhmfl.gov/movies/levitation/index.htmlMagnetic properties of materialsMagnetic properties of materialsFerromagnetismFerromagnetismInteractionInteractionInteraction results in a tendency for magnetic moments to align Interaction results in a tendency for magnetic moments to align below below some characteristic temperature called the some characteristic temperature called the Curie temperatureCurie temperature..This is not aclassicalphenomenon.Ferromagnetismis in fact very rare.Nature doesnNature doesn’’t like this situationt like this situationFerromagnetismFerromagnetismInteractionInteractionShort range quantum mechanical interaction favors Short range quantum mechanical interaction favors alignment. However, this costs energy on large alignment. However, this costs energy on large length scaleslength scalesInteractionInteraction202Buμ=Application of a magnetic
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